Question

Please simplify this log I really really need the answer asap

Answer 1

step 1

Simplify the interior expression in the log

so

we have

$\frac{\frac{\frac{a^2g^7z^8}{b^{(12)}d^{(45)}}}{\sqrt[3]{xy}z^{(23)}}}{\frac{w^2p^5}{\frac{\sqrt{r}tv^7}{b}}}$$\frac{\frac{\frac{a^{2}g^{7}z^{8}}{b^{(12)}d^{(45)}}}{\sqrt[3]{xy}z^{(23)}}}{\frac{w^2p^5}{\frac{\sqrt{r}tv^7}{b}}}\frac{}{}=\frac{\frac{a^2g^7z^8}{b^{(12)}d^{(45)}}}{\sqrt[3]{x}yz^{(23)}}\div\frac{w^2p^5}{\frac{\sqrt{r}tv^7}{b}}=\frac{\frac{a^2g^7z^8}{b^{(12)}d^{(45)}}*\frac{\sqrt{r}tv^7}{b}}{\sqrt[3]{x}yz^{(23)}*w^2p^5}$$\frac{\frac{a^{2}g^{7}z^{8}}{b^{(12)}d^{(45)}}\frac{\sqrt{r}tv^7}{b}}{\sqrt[3]{xy}z^{(23)}w^2p^5}=\frac{\frac{a^2g^7z^8r^{(\frac{1}{2})}tv^7}{b^{(13)d(45)}}}{\sqrt[3]{xy}z^{(23)}w^2p^5}=\frac{a^2g^7z^8r^{(\frac{1}{2})}tv^7}{b^{(13)}d^{(45)}}\div\sqrt[3]{xy}z^{(23)}w^2p^5=\frac{a^2g^7z^8r^{(\frac{1}{2})}tv^7}{b^{(13)}d^{(45)}\sqrt[3]{xy}z^{(23)}w^2p^5}$$\frac{a^2g^7z^8r^{(1\/2)}tv^7}{b^{(13)}d^{(45)}\sqrt[3]{xy}z^{(23)}w^2p^5}=\frac{a^2g^7r^{(1\/2)}tv^7}{b^{(13)}d^{(45)}\sqrt[3]{xy}z^{(15)}w^2p^5}$

we have the expression

$log(\frac{a^2g^7r^{(\frac{1}{2})}tv^7}{b^{(13)}d^{(45)}\sqrt[3]{xy}z^{(15)}w^2p^5})=log(a^2g^7r^{(\frac{1}{2})}tv^7)-log(b^{(13)}d^{(45)}\sqrt[3]{xy}z^{(15)}w^2p^5)$

Simplify the first term

$log(a^2g^7r^{(\frac{1}{2})}tv^7)=loga^2+logg^7+logr^{(\frac{1}{2})}+logt+logv^7$$loga^2+logg^7+logr^{(\frac{1}{2})}+logt+logv^7=2loga+7logg+\frac{1}{2}logr+logt+7logv$

Simplify the second term

$log(b^{(13)}d^{(45)}\sqrt[3]{xy}z^{(15)}w^2p^5)=logb^{(13)}+logd^{(45)}+log\sqrt[3]{xy}+logz^{(15)}+logw^2+logp^5$$logb^{(13)}+logd^{(45)}+log\sqrt[3]{xy}+logz^{(15)}+logw^2+logp^5=13logb+45logd+\frac{1}{3}logxy+15logz+2logw+5logp$

Substitute in expression

$\begin{gathered} log(a^2g^7r^{(\frac{1}{2})}tv^7)-log(b^{(13)}d^{(45)}\sqrt[3]{xy}z^{(15)}w^2p^5) \\ (2loga+7logg+\frac{1}{2}logr+logt+7logv)-(13logb+45logd+\frac{1}{3}logxy+15logz+2logw+5logp) \end{gathered}$